Shortcuts to Spherically Symmetric Solutions: A Cautionary Note

TL;DR

This paper warns against overusing a shortcut method for deriving spherically symmetric solutions in gravitational models, emphasizing the importance of proper ansatz choices to avoid invalid results.

Contribution

It highlights the limitations of the one-function ansatz in deriving correct spherically symmetric solutions, providing cautionary guidance for gravitational research.

Findings

One-function ansatz can lead to incorrect solutions.

Proper metric component treatment is essential for valid solutions.

The paper illustrates potential pitfalls with specific examples.

Abstract

Spherically symmetric solutions of generic gravitational models are optimally, and legitimately, obtained by expressing the action in terms of the two surviving metric components. This shortcut is not to be overdone, however: a one-function ansatz invalidates it, as illustrated by the incorrect solutions of [1].